Publicado

2015-07-01

Bootstrap-based inference for grouped data

Inferencia para datos agrupados vía bootstrap

DOI:

https://doi.org/10.15446/rev.fac.cienc.v4n2.54254

Palabras clave:

Bootstrap, estimation, grouped Data (en)
Bootstrap, datos agrupados, estimación (es)

Descargas

Autores/as

  • Jorge Iván Vélez Australian National University
  • Juan Carlos Correa Morales
Grouped data refers to continuous variables that are partitioned in intervals, not necessarily of the same length, to facilitate its interpretation.  Unlike in ungrouped data, estimating simple summary statistics as the mean and mode, or more complex ones as a percentile or the coefficient of variation, is a difficult endeavour in grouped data. When the probability distribution generating the data is unknown, inference in ungrouped data is carried out using parametric or nonparametric resampling methods. However, there are no equivalent methods in the case of grouped data.  Here, a bootstrap-based procedure to estimate the parameters of an unknown distribution based on grouped data is proposed, described and illustrated.

Los datos agrupados se reeren a variables continuas que se dividen en intervalos no necesariamente de la misma longitud para facilitar su interpretación. Contrario a lo que ocurre en datos no agrupados, la estimación de simples estadísticos de resumen como la media o la moda, o más complejos como un percentil o el coeciente de variación, es una tarea difícil en datos agrupados. Cuando no se conoce la distribución de probabilidad que genera los datos, la inferencia en datos no agrupados se realiza utilizando métodos paramétricos o no paramétricos de remuestreo. Sin embargo, no existen métodos equivalentes para datos agrupados. En este documento se propone, describe e ilustra un método basado en bootstrap para estimar los parámetros de una distribución desconocida a partir de datos agrupados.

Referencias

Carpenter, J. & Bithell, J. (2000), Bootstrap Confidence Intervals: When, Which, What? A Practical Guide for Medical Statisticians, Statistics in Medicine, 19(9), 1141-1164.

Davison, A. C.; Hinkley, D. V. & Young, G. A. (2003), Recent Developments in Bootstrap Methodology, Statistical Science, 18(2), 141-157.

DiCiccio, T. J. & Efron, B. (1996), Bootstrap Confidence Intervals, Statistical Science, 11 (3), 189-228.

Efron, B. (1979), Bootstrap Methods: Another Look at the Jackknife, The Annals of Statistics, 7 (1), 1-27.

Efron, B. (1987), Better Bootstrap Confidence Intervals, Journal of the American Statistical Association, 82 (397), 171-185.

Efron, B. (2003), Second Thoughts on the Bootstrap, Statistical Science, 18( 2), 135-140.

Hajargasht, G.; Gri_ths, W. E.; Brice, J. & Rao, D. P. & Chotikapanich, D. (2012), Inference for income distributions using grouped data, Journal of Business & Economic Statistics, 30( 4), 563-575.

Harrell, F. E. & Davis, C. E. (1982), A New Distribution-Free Quantile Estimator, Biometrika, 69( 3), 635-640.

Heitjan, D. F. (1989), Inference from grouped continuous data: A review, Statistical Science, 4(2), 164-179.

Hinkley, D. V. (1988), Bootstrap Methods, Journal of the Royal Statistical Society. Series B (Methodological), 50(3), 321-337.

Kanazawa, Y. (1992), An Optimal Variable Cell Histogram Based on the Sample Spacings, The Annals of Statistics, 20 (1), 291-304.

Letson, D. & McCullogh, B. D. (1998), Better Confidence Intervals: The Double Bootstrap with No Pivot, American Journal of Agricultural Economics, 80(3), 552-559.

On, C. W. (2002), Mean, Variance and Standard Deviation for Grouped Data, http://www.angelfire.com/blues/michaelyang/ive/dms/chapter_05/5_6_StaDev.html. Accessed: 2015-11-18.

Pierce, R. (2014), Mean, Median and Mode from Grouped Frequencies, https://www.mathsisfun.com/data/frequency-grouped-mean-median-mode.html. Accessed: 2015-11-18.

R Core Team (2015), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org/.

Scott, D. W. (1979), On Optimal and Data-Based Histograms, Biometrika, 66 (3), 605-610.

Scott, D. W. & Scott, W. R. (2008), Smoothed Histograms for Frequency Data on Irregular Intervals, The American Statistician, 62(3), 256-261.

Taylor, C. C. (1987), Akaike's Information Criterion and the Histogram, Biometrika, 74(3), 636-639.

Vélez, J. I. & Correa, J. C. (2014), Should we think of a different Median estimator?, Revista Comunicaciones en Estadística, 7( 2), 1-8.

Wand, M. P. (1997), Data-based Choice of Histogram Bin Width, The American Statistician, 51(1), 59-64.

Zhan, Y. & Wellner, J. A. (1995), Double censoring: characterization and computation of the nonparametric maximum likelihood estimator, Technical report.

Dimensions

PlumX

Visitas a la página del resumen del artículo

872

Descargas

Los datos de descarga aún no están disponibles.

Cómo citar

Inferencia para datos agrupados vía bootstrap. (2015). Revista De La Facultad De Ciencias, 4(2), 74-82. https://doi.org/10.15446/rev.fac.cienc.v4n2.54254